Predators–prey models with competition, Part I: Existence, bifurcation and qualitative properties

DOI10.1142/S0219199718500104zbMath1404.35452arXiv1712.01891WikidataQ115523118 ScholiaQ115523118MaRDI QIDQ4554618

Alessandro Zilio, Henri Berestycki

Publication date: 9 November 2018

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1712.01891

zbMATH Keywords

optimizationcompetitionasymptotic analysisstability of solutionsbifurcation analysissystems of parabolic equationsnon-constant solutions

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Singular perturbations in context of PDEs (35B25) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Population dynamics (general) (92D25) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Bifurcations in context of PDEs (35B32) Animal behavior (92D50)

Related Items (7)

Traveling wave solutions in predator–prey models with competition ⋮ Local existence of solutions to a nonlinear autonomous PDE model for population dynamics with nonlocal transport and competition ⋮ On a two-species competitive predator-prey system with density-dependent diffusion ⋮ Some remarks on segregation of \(k\) species in strongly competing systems ⋮ Qualitative features of a nonlinear, nonlocal, agent-based PDE model with applications to homelessness ⋮ On the limit configuration of four species strongly competing systems ⋮ Boundedness and global stability of the predator-prey model with prey-taxis and competition

Cites Work

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• Some global results for nonlinear eigenvalue problems
• Dynamics of strongly competing systems with many species
• Asymptotic Behaviors of a Parabolic System Related to a Planktonic Prey and Predator Model
• Diffusion and the Predator-Prey Interaction
• Large Time Behavior of Solutions of Systems of Nonlinear Reaction-Diffusion Equations
• A variational problem for the spatial segregation of reaction-diffusion systems
• Bifurcation Theory in Real Banach Space
• Bifurcation Theory for Analytic Operators

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